A security issue in multi-sensor systems is investigated from the standpoint of a malicious attacker. The considered system is equipped with a decentralized Kalman filter and chi^2 detectors. A malicious attacker intends to destroy the system performance by modifying the measurement innovation. To damage the system performance as much as possible, we derive the subsystems error covariances in the form of mathematical expectations and then quantify their relation with the error covariance of the fused system. Furthermore, by utilizing the matrix theory, we analyze the difference of performance metrics before and after an attack. And the optimal linear deception attack strategy can be obtained, which can successfully avoid being detected by the chi^2 detector. Finally, a numerical example is given to demonstrate the effectiveness of the proposed attack strategy.